A common door usually has only one lock, and for higher safety a second lock, i.e. an auxiliary lock is added. For example, U.S. Pat. Nos. 3,990,277, 4,129,019, 4,183,563, 4,418,552 and 4,709,565 devised two locks to be locked and unlocked at the same time, and the lock added is the auxiliary lock which is to be rotated to open a door with a key from outside and to be rotated to open the door by rotating after pushing a turning button from inside. Therefore, firmness and hardness of the auxiliary lock is especially considered important, and developed countries have an industrial testing standard for it, such as punching test, a pulling test, a torque test, etc, so an auxiliary lock has to pass those tests for preventing it from illegal breakage. To attain this purpose, those patents mentioned above mostly have comparatively a hard housing made of cast for containing a latch unit, to a resultant rather high cost. But they still can hardly pass the torque test, that is, the latch unit cannot resist boring of more than two holes in it and the latch is forcibly rotated illegally by means of a tool like a wrench to open the door.